Abstract composition rule for relativistic kinetic energy in the thermodynamical limit

Details Abstract composition rule for relativistic kinetic energy in the thermodynamical limit Abstract composition rule for relativistic kinetic energy in the thermodynamical limit

2008-09-26

arxiv.org/abs/0809.4675v1

Europhys.Lett.84:56003,2008

Physics

Nuclear Physics

Nuclear Theory

Submitted to Europhysics Letters. LaTeX, 3 eps figures

Scientific paper

10.1209/0295-5075/84/56003

We demonstrate by simple mathematical considerations that a power-law tailed distribution in the kinetic energy of relativistic particles can be a limiting distribution seen in relativistic heavy ion experiments. We prove that the infinite repetition of an arbitrary composition rule on an infinitesimal amount leads to a rule with a formal logarithm. As a consequence the stationary distribution of energy in the thermodynamical limit follows the composed function of the Boltzmann-Gibbs exponential with this formal logarithm. In particular, interactions described as solely functions of the relative four-momentum squared lead to kinetic energy distributions of the Tsallis-Pareto (cut power-law) form in the high energy limit.

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